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For the following questions, let V be the set of vertices in the graph below, and let E be the set of edges. Answer the following questions 1- a f m be th k e 1. Write V in roster form. 2. Compute |EJ. 3. Let R = {x € V| there is a path from a to x}. Write R' in roster form.

For the following questions, let V be the set of vertices in the graph below, and let E be the set of edges. Answer the following questions 1- a f m be th k e 1. Write V in roster form. 2. Compute |EJ. 3. Let R = {x € V| there is a path from a to x}. Write R' in roster form.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the following questions, let V be the set of vertices in the graph below, and let E be the set of edges. Answer the following questions 1-9. a f m b k e 1. Write V in roster form. 2. Compute |EJ. 3. Let R = {x E V| there is a path from a to x}. Write R' in roster form. 4. Let D3 = {x EV| x has degree 3} and let T = {x E V|x is part of a triangular subgraph}. Does D3 =T? Prove or disprove. 5. Let D4 = {x €V|x has degree 4}. Write D4 U (D3 nT) in roster form. 6. Write R in terms of D3 and D4. 7. Let N = {a, h, i, c}. Using the fact that each of these vertices shares an edge with b, write N in set-builder form. 8. Write {a, h, c} in terms of N and D3. 9. Let N x R' = {(x, y) | x e N and y e R' }. Write N x R' in roster form.
Transcribed Image Text:For the following questions, let V be the set of vertices in the graph below, and let E be the set of edges. Answer the following questions 1-9. a f m b k e 1. Write V in roster form. 2. Compute |EJ. 3. Let R = {x E V| there is a path from a to x}. Write R' in roster form. 4. Let D3 = {x EV| x has degree 3} and let T = {x E V|x is part of a triangular subgraph}. Does D3 =T? Prove or disprove. 5. Let D4 = {x €V|x has degree 4}. Write D4 U (D3 nT) in roster form. 6. Write R in terms of D3 and D4. 7. Let N = {a, h, i, c}. Using the fact that each of these vertices shares an edge with b, write N in set-builder form. 8. Write {a, h, c} in terms of N and D3. 9. Let N x R' = {(x, y) | x e N and y e R' }. Write N x R' in roster form.
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